Trial and Improvement

Venn Diagrams

Reflect a shape

Rotate a shape

Translate a shape Across Up or Down

ENLARGEMENT Scale factor x3 Count across and up from the centre Times this by 3 from the centre Negative enlargement goes the opposite way

POLYGON ANGLES Interior angle is 180 – exterior angle

CIRCLE THEOREM o o o xo xo ao 2xo bo yo yo xo xo yo DIAMETER RADIUS 8 a + b = 180° x + y = 180° Angle at centre is twice the angle at the circumference. Angle made by a diameter is 90°. Opposite angles in a cyclic quadrilateral add up to 180° xo yo o RADIUS xo yo Angles subtended by an arc or a chord in the same segment are equal. Alternate segment theorem. Angle between a tangent and a radius make 90° 8

Two brackets together – eyebrows and smiley face are 4 multiplies EXPANDING BRACKETS Two brackets together – eyebrows and smiley face are 4 multiplies 9

Pick the x’s to times together FACTORISING BRACKETS Pick the x’s to times together Pick the numbers to times to the question Check the smiley face to see if the x term is right 10

FORM AND SOLVE EQUATION This one is about angles, so add algebra together and put equal to 360. If perimeter, do the same but put = perimeter. Solve by simplifying and solving

PLOTTING GRAPHS Complete table of values Plot points on grid Join points together to make a graph

PROPORTION Bring in k Y = k x2 Work out k If inverse proportion, Y = k

Nth Term Find the nth term of the following sequences and then calculate the 100th term. a) 3, 7, 11, 15, … Nth term so far = 4n +4 Start number is -1 Nth term is 4n - 1 Worksheet needs printing 100th term = 4x100 -1 100th term = 399 14

Draw line 2x -3y = 6 by making a table Pick a point not on the line Take the x and y numbers and put into the inequality. See if the inequality is true or false for that side

ESTIMATE OF THE MEAN 2 extra columns Use mid point of groups Mid point x frequency Big total divided by little total

PRIME FACTOR TREES PRIME NUMBERS 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, … EXAMPLES Find the product of prime factors for the following numbers: (a) 32 (b) 60 8 4 10 6 4 2 2 2 5 2 3 2 2 2 ANSWER = 2 X 2 X 3 X 5 ANSWER = 2 X 2 X 2 X 2 X 2 = = X 3 X 5 17

PYTHAGORAS TAKE THE 2 NUMBERS SQUARE ADD OR SUBTRACT SQUARE ROOT

Area of Isosceles Triangle Use Pythagoras to find the height Then use base x height / 2 for the area

TRIG Right angle triangle Label sides Opp Adj Tan Opp Hyp Sin Adj Hyp Cos Right angle triangle Label sides Pick correct triangle Cover up the side you want If finding angle use the 2ndF button Write SOHCAHTOA on the formula page of the paper